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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 5390.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5390.h1 | 5390s1 | \([1, 1, 0, -4337, -112811]\) | \(-76711450249/851840\) | \(-100218124160\) | \([]\) | \(6552\) | \(0.92576\) | \(\Gamma_0(N)\)-optimal |
5390.h2 | 5390s2 | \([1, 1, 0, 14528, -569344]\) | \(2882081488391/2883584000\) | \(-339250774016000\) | \([]\) | \(19656\) | \(1.4751\) |
Rank
sage: E.rank()
The elliptic curves in class 5390.h have rank \(0\).
Complex multiplication
The elliptic curves in class 5390.h do not have complex multiplication.Modular form 5390.2.a.h
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.